4 ms·

I'll leave this quote here as my response: > There is a most profound and beautiful question associated with the observed coupling constant, e – the amplitude

I'll leave this quote here as my response: > There is a most profound and beautiful question associated with the observed coupling constant, e – the amplitude for a real electron to emit or absorb a real photon. It is a simple number that has been experimentally determined to be close to 0.08542455. (My physicist friends won't recognize this number, because they like to remember it as the inverse of its square: about 137.03597 with about an uncertainty of about 2 in the last decimal place. It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it.) Immediately you would like to know where this number for a coupling comes from: is it related to pi or perhaps to the base of natural logarithms? Nobody knows. It's one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say the "hand of God" wrote that number, and "we don't know how He pushed his pencil." We know what kind of a dance to do experimentally to measure this number very accurately, but we don't know what kind of dance to do on the computer to make this number come out, without putting it in secretly! — Richard Feynman, Richard P. Feynman (1985). QED: The Strange Theory of Light and Matter. Princeton University Press. p. 129. ISBN 978-0-691-08388-9. [my emphasis added]

T-A 8y ago
I have never seen a physicist put that particular number on a wall (these days, the cosmological constant would be a better bet). I am vaguely aware of numerological attempts (some collected in [1]) to "explain" why 137 is "special", none of which has ever led anywhere. As far as I can tell, the fascination with it got started by the number being close to an integer, and maybe the remark in [1] that "In ancient Hebraic language letters where used for numbers, and Cabbala is the word corresponding to 137" played a role. But we know that it isn't an integer, and that it runs [2] like any coupling constant in QFT, so at best you could marvel about it taking on some particular value at some particular interaction energy, which would mean... what? I dunno. As Feynman also said [3], You know, the most amazing thing happened to me tonight... I saw a car with the license plate ARW 357. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight? Amazing! [1] https://arxiv.org/abs/1009.1711 https://arxiv.org/abs/1009.1711 [2] https://en.wikipedia.org/wiki/Coupling_constant#Running_coupling https://en.wikipedia.org/wiki/Coupling_constant#Running_coup... [3] https://www.goodreads.com/quotes/649893-you-know-the-most-amazing-thing-happened-to-me-tonight https://www.goodreads.com/quotes/649893-you-know-the-most-am...
- jsweojtj 8y ago
  Your latest comment seems to be replying to someone with a fascination with the specific number 1/137, which I do not have, and some related tangents. I'll try to refocus the points of contention between us. This whole thread started because the top comment said that a physics theory predicted the value of the fine-structure constant. Which is wrong, as the fine-structure constant is one of fundamental constants of the universe and one _whose value is not predicted by any theory_. At this stage, two claims are in tension. The first is your claim, that QED predicts the fine-structure constant once you measure the magnetic moment of the electron using several thousand Feynman diagrams. The second claim is Feynman, himself, literally writing in his book titled _QED_, that we have no idea how to predict the value of this constant. Could it be that Feynman overlooked the fact that he, himself, predicted the value of the fine-structure constant? He thought that not being able to predict its value was such an unsolved problem as to call it "one of the greatest damn mysteries of physics"? That "all good theoretical physicists put this number up on their wall and worry about it"? The long and the short of it is that I think you're missing something much deeper. Yes, _once you measure_ something that has a tight coupling with the fine-structure constant, you now know the value of the fine-structure constant. But, before you made that measurement you DO NOT KNOW and further CANNOT PREDICT the value of the fine-structure constant. If you could, you'd be able to claim your own Nobel prize.
  - T-A 8y ago
    > This whole thread started because the top comment said that a physics theory predicted the value of the fine-structure constant. Yes. > Which is wrong No. I even provided you with the reference to the paper in question. Did you even try to read it? > as the fine-structure constant is one of fundamental constants of the universe and one _whose value is not predicted by any theory_ This is where you go wrong, and where you misunderstand Feynman's point. The correct statement is that all respectable theories of physics (to date), including the Standard Model, include an irreducible number of values which must be plugged into them "by hand". In other words, once you've written down your theory, there are some parameter values in it about which the theory itself gives you no guidance; you could give them different values, and the theory would still work. It would just be describing a universe with different properties than ours. In order to make it describe our universe, you need to get those values from experiment. Feynman's point is that we don't have a theory without at least some such parameters (even string theory, which he disliked, has the string tension, and it skirts the need for more by randomly picking a vacuum, which sets the values of low energy theory "constants"). It is not that the fine structure constant has some particular status as "more fundamental" than others. The choice of constants which you can determine by experiment is constrained by the theory, but generally not locked down completely; you can choose your set of constants, as long as they are independent, i.e. as long as measured constant #1 can not be determined by plugging measured constant #2 into the theory and doing some calculation. If constant #1 can be computed given the theory and constant #2, then they are not independent, and the choice between them is arbitrary; a convention. The choice between fine structure constant and magnetic moment of the electron is one such arbitrary choice. Given one of them and the Standard Model, you can compute the other. And It turns out that it's actually more convenient to do it this way: measure the magnetic moment, then compute the fine structure constant. There is no reason at all to regard the fine structure constant as more of an "input to the model" than the magnetic moment, as you claimed at the start of this thread. Needless to say, Feynman knew all this perfectly well. You are just taking away the wrong message from an attempt to popularize the topic. "QED" was a popular book, not a graduate text.

T-A 8y ago

I have never seen a physicist put that particular number on a wall (these days, the cosmological constant would be a better bet). I am vaguely aware of numerological attempts (some collected in [1]) to "explain" why 137 is "special", none of which has ever led anywhere. As far as I can tell, the fascination with it got started by the number being close to an integer, and maybe the remark in [1] that "In ancient Hebraic language letters where used for numbers, and Cabbala is the word corresponding to 137" played a role. But we know that it isn't an integer, and that it runs [2] like any coupling constant in QFT, so at best you could marvel about it taking on some particular value at some particular interaction energy, which would mean... what? I dunno. As Feynman also said [3], You know, the most amazing thing happened to me tonight... I saw a car with the license plate ARW 357. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight? Amazing! [1] https://arxiv.org/abs/1009.1711 https://arxiv.org/abs/1009.1711 [2] https://en.wikipedia.org/wiki/Coupling_constant#Running_coupling https://en.wikipedia.org/wiki/Coupling_constant#Running_coup... [3] https://www.goodreads.com/quotes/649893-you-know-the-most-amazing-thing-happened-to-me-tonight https://www.goodreads.com/quotes/649893-you-know-the-most-am...

jsweojtj 8y ago
Your latest comment seems to be replying to someone with a fascination with the specific number 1/137, which I do not have, and some related tangents. I'll try to refocus the points of contention between us. This whole thread started because the top comment said that a physics theory predicted the value of the fine-structure constant. Which is wrong, as the fine-structure constant is one of fundamental constants of the universe and one _whose value is not predicted by any theory_. At this stage, two claims are in tension. The first is your claim, that QED predicts the fine-structure constant once you measure the magnetic moment of the electron using several thousand Feynman diagrams. The second claim is Feynman, himself, literally writing in his book titled _QED_, that we have no idea how to predict the value of this constant. Could it be that Feynman overlooked the fact that he, himself, predicted the value of the fine-structure constant? He thought that not being able to predict its value was such an unsolved problem as to call it "one of the greatest damn mysteries of physics"? That "all good theoretical physicists put this number up on their wall and worry about it"? The long and the short of it is that I think you're missing something much deeper. Yes, _once you measure_ something that has a tight coupling with the fine-structure constant, you now know the value of the fine-structure constant. But, before you made that measurement you DO NOT KNOW and further CANNOT PREDICT the value of the fine-structure constant. If you could, you'd be able to claim your own Nobel prize.
- T-A 8y ago
  > This whole thread started because the top comment said that a physics theory predicted the value of the fine-structure constant. Yes. > Which is wrong No. I even provided you with the reference to the paper in question. Did you even try to read it? > as the fine-structure constant is one of fundamental constants of the universe and one _whose value is not predicted by any theory_ This is where you go wrong, and where you misunderstand Feynman's point. The correct statement is that all respectable theories of physics (to date), including the Standard Model, include an irreducible number of values which must be plugged into them "by hand". In other words, once you've written down your theory, there are some parameter values in it about which the theory itself gives you no guidance; you could give them different values, and the theory would still work. It would just be describing a universe with different properties than ours. In order to make it describe our universe, you need to get those values from experiment. Feynman's point is that we don't have a theory without at least some such parameters (even string theory, which he disliked, has the string tension, and it skirts the need for more by randomly picking a vacuum, which sets the values of low energy theory "constants"). It is not that the fine structure constant has some particular status as "more fundamental" than others. The choice of constants which you can determine by experiment is constrained by the theory, but generally not locked down completely; you can choose your set of constants, as long as they are independent, i.e. as long as measured constant #1 can not be determined by plugging measured constant #2 into the theory and doing some calculation. If constant #1 can be computed given the theory and constant #2, then they are not independent, and the choice between them is arbitrary; a convention. The choice between fine structure constant and magnetic moment of the electron is one such arbitrary choice. Given one of them and the Standard Model, you can compute the other. And It turns out that it's actually more convenient to do it this way: measure the magnetic moment, then compute the fine structure constant. There is no reason at all to regard the fine structure constant as more of an "input to the model" than the magnetic moment, as you claimed at the start of this thread. Needless to say, Feynman knew all this perfectly well. You are just taking away the wrong message from an attempt to popularize the topic. "QED" was a popular book, not a graduate text.